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The asymptotic trace norm of random circulants and the graph energy

100%

Koshkin S.

Discussiones Mathematicae Probability and Statistics

2016

tom 36

nr 1-2

67-92

We compute the expected normalized trace norm (matrix/graph energy) of random symmetric band circulant matrices and graphs in the limit of large sizes, and obtain explicit bounds on the rate of convergence to the limit, and on the probabilities of large deviations. We also show that random symmetric band Toeplitz matrices have the same limit norm assuming that their band widths remain small relative to their sizes. We compare the limit norms across a range of related random matrix and graph ensembles.

Binomial ARMA count series from renewal processes

63%

Koshkin S., Cui Y.

Discussiones Mathematicae Probability and Statistics

2012

tom 32

nr 1-2

5-16

This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration.

Ograniczanie wyników

2 Discussiones Mathematicae Probability and Statistics

2 Koshkin S.

1 Cui Y.

1 2016

1 2012

Wyniki wyszukiwania

The asymptotic trace norm of random circulants and the graph energy

Binomial ARMA count series from renewal processes